Making Medical Math fun and EASY!A Veterinary Guide to Medical Math

Jessica Griffith, RVT jjgriff@iastate.edu Small Animal ICU Technical Supervisor Iowa State University College of Veterinary Medicine

About Me

! Born and raised in Iowa ! Moved to Michigan in 2011 ! Graduated with AAS in Veterinary

Technology in 2015 ! Worked in private practice ER clinic for 1

year ! Moved back to Iowa in 2016 ! Began working at ISU in the Small Animal

ICU in 2016 ! Became ICU Veterinary Technical

Supervisor in 2018

https://www.bestplaces.net/city/iowa/de_witt http://www.westplainsengineering.com/2012/09/iowa-state-university-college-of-veterinary-medicine-2/

Today’s Medical Math FUNThe Basics

! Converting units ! Weight ! Concentration ! Volume

! Basic drug dose ! IV Fluid rates

! Fluid pumps ! Manual drip rates

! Dextrose Supplementation

Advanced Medical Math! Constant-rate infusions

! Delivery rates ! Pumps ! Manual drip rates

! Electrolyte supplementation

MATH !

" YOU

https://clawguard.com/blogs/clawguard-blog/80377222-is-my-dog-stressed

1. Patient 2. Drug 3. Dose 4. Route 5. Frequency

The 5 “Rights”

“Give 2 capsules twice daily”

“2 drops in

effected eye as

needed”

http://www.worldwhiteweb.net/

Complete Prescription Instructions

“2 drops in effected eye as needed”

Instill 2 drops into the left eye up to every 4 hours as needed for 2

weeks

“Give 2 capsules twice daily”

Give 2 capsules by mouth every 12 hours until gone

Dose vs Dosage

Dose = a specific amount of medication administered at one time • Example: 400 mg (2 capsules) ibuprofen

Dosage = the specific amount, number, or frequency of doses over a period of time • Example: 400 mg ibuprofen every 12

hours for two days Day 1: Day 2:

Conversions to Know

1. pounds kilograms

2. milligrams micrograms

3. grams milliliters

https://www.wikihow.com/Convert-Milliliters-(mL)-to-Grams-(g)

1 kilogram

1 pound

A Few Methods to Write Out Math Equations! Classic Equation

! Lines & Cancelling Units ! 14 kg 2 mg 1 mL 1 kg 10 mg

! Shifting Decimal Places !280 ÷ 1000 = 280.0 = 0.28

= 2.8 mL

https://www.rd.com/culture/math-lessons-real-life/

Pounds Kilograms

!2.2 pounds (lb) = 1 kilogram (kg) !Pounds to kilograms (kg)

! lb ÷ 2.2 = kg

!Kilograms (kg) to pounds !kg x 2.2 = Lb

1 lb. 1 lb.0.2 lb. 1 kg

http://www.mathwatson.com/professional-bathroom-scales.html

Example 1Kilograms to Pounds Pounds to Kilograms

! How many pounds does a 17 kilogram dog weight?

! How many kilograms does a 17 pound dog weigh?

https://www.cuteness.com/article/differences-between-english-british-bulldogs

1 kilogram (kg) = 1000 grams (g)

! Kilograms (kg) to grams (g)

! kg x 1000 = g

! Grams (g) to kilograms (kg)

! g ÷ 1000 = kg

Example 2: How many kilograms does a 578 gram guinea pig weigh?

5 7 8.0 grams

0.578 kilograms

Kilograms

Grams

https://flipboard.com/@kristinapor41nk/guinea-pig-info-k6tgl2vrz

Putting it Together

Example 3: How many pounds does a 0.578 kg guinea pig weigh?

OR

0.578 × 2.2 = 1.27 pounds

Milligrams Micrograms

! 1 milligram (mg) = 1,000 micrograms (mcg) ! 1 microgram (mcg) = 0.001 milligrams (mg)

!Milligrams to micrograms !mg x 1,000 = mcg

!Micrograms to milligrams !mcg ÷ 1,000 = mg

2.18 mg x 1000= 2.180 mcg = 2180 mcg

ExamplesExample 1: How many micrograms of dexmedetomidine are in 0.4 mL of an injectable solution with a concentration of 0.5 mg/mL? 1. Calculate how many milligrams in 0.4 milligrams

2. Calculate how many micrograms are in 0.2 milligrams by multiplying by 1000

= 0.5 mg1 mL

0.4 mL = 0.2 mg

0.200 x 1000 =

200 mcg

2.400 x 1000 = 2400 mcg

Examples

Example 2: How many micrograms are in 2.4 milligrams?

= 2400 mcg

Grams Milliliters Liters Kilograms

Did you know?

Weight to Volume (of Water)

o Grams to milliliters o 1 gram = 1 milliliter

o Liters to kilograms

o 1 liter = 1 kilogram

https://www.guidedogsvictoria.com.au/shop/ https://makeyourbodywork.com/drink-water-to-lose-weight/

8 kg puppy

≈

DrugDoseCalculations

https://spyescapeandevasion.com/blog/2016/08/15/why-ghost-apps-are-so-dangerous/

When cell phone use is encouraged!

Basic Drug Dose CalculationsA 28 pound mixed breed canine needs a 2 milligrams per kilogram dose of furosemide. The available concentration is 5%. What volume will this dog receive per dose?

Concentration % × 10 = mg/mL

5 ×10 = 50 mg/mL

Basic Drug Dose CalculationsA 28 pound mixed breed canine needs a 2 milligrams per kilogram dose of furosemide. The available concentration is 5%. What volume will this dog receive per dose?

1. Convert pounds to kilograms 12.7 kilograms

Basic Drug Dose CalculationsA 28 pound mixed breed canine needs a 2 milligrams per kilogram dose of furosemide. The available concentration is 5%. What volume will this dog receive per dose? 1. Convert pounds to kilograms

12.7 kilograms

2. Multiply by dosage (mg/kg)

Basic Drug Dose CalculationsA 28 pound mixed breed canine needs a 2 milligrams per kilogram dose of furosemide. The available concentration is 5%. What volume will this dog receive per dose?

1. Convert pounds to kilograms 12.7 kilograms

2. Multiply by dosage (mg/kg)

3. Divide by drug concentration (mg/mL) 0.51 milliliters

All Together Now!

28 lbs 1 kg 2 mg 1 mL 2.2 lbs 1 kg 50 mg

Steps: 1. Convert pounds to

kilograms 2. Multiply by dosage

(mg/kg) 3. Divide by drug

concentration (mg/mL)

= 0.51 mLOR

https://weheartit.com/entry/11357611

IV Fluid RatesFluid Pumps

! Need to know: 1. Rate (mL/hr)

2. Volume to be infused (mL)

http://apexx-equipment.com/pre-owned-vet-equipment/iv-pumps/Baxter-Flo-Gard-6200-IV-Pump https://www.adeptomed.com/product/buy-service-rent/hospira-plum-a-11-6 https://heska.com/products/iv-pumps/vet-iv-infusion-pump.aspx?s=0BC104F55A4DD097D3EF5B416513501161B465BC

IV Fluid RatesManual Drip Sets

! Need to know: 1. Rate (mL/hr)

2. Volume to be infused (mL)

3. Drops/mL of fluid line

https://basicmedicalkey.com/basic-intravenous-therapy-calculations/

Components to Calculate Daily Fluid Rates:

1.Maintenance 2.Fluid deficit 3.Ongoing losses

https://www.pepperlaw.com/publications/not-so-simple-math-calculating-the-regulatory-review-period-for-patent-term-extension-2017-05-18/

Calculating Daily Fluid Rates

1. Maintenance – includes normal sensible and insensible losses

https://www.animalbehaviourbusiness.com/wet-greetings/ https://www.akc.org/expert-advice/health/doggie-diarrhea/ https://barkingroyalty.com/dog-panting-and-shaking/

Calculating Daily Fluid Rates

1. Maintenance – includes normal sensible and insensible losses

70×[body weight(kg)0.75]

40-60 mL/kg/day

Calculating Daily Fluid Rates

1. Maintenance 2. Fluid deficit – as assessed using hydration parameters

https://www.fieldandstream.com/blogs/mans-best-friend/2011/06/how-tell-if-your-dog-dehydrated

Calculating Daily Fluid Rates

[Body weight (kg) × percent dehydration (decimal)] × 1000 = mL deficit

1. Maintenance 2. Fluid deficit – as assessed using hydration parameters

Calculating Daily Fluid Rates

1. Maintenance 2. Fluid deficit 3. Ongoing losses – estimation of volume continuing to be lost

http://www.summit107.com/news/east-kootenay-news/warning-of-potentially-fatal-canine-parvovirus-in-the-elk-valley/ https://www.medvetforpets.com/management-of-feline-lower-urinary-tract-disorder-flutd/

Calculating Daily Fluid Rates

1. Maintenance 2. Fluid deficit 3. Ongoing losses – estimation of volume continuing to be lost

(mL per hour ×24 hours)=mL of daily ongoing losses

Calculating Daily Fluid RatesMaintenance

Deficit [Body weight (kg) x percent dehydration (decimal)] x 1000

Ongoing Losses mL/day

volume (mL) to be administered over the next 24 hours

Hank, 4 YO CM German Shepherd Presenting for vomiting x 3 days -44 kg -5% dehydrated, to be corrected over 12 hours -estimated to be vomiting ~30 mL/hr

Maintenance = 1196 mL/day

Deficit Ongoing Losses

= 4116 mL

Hank

Maintenance = 1196 mL/day

Deficit = over 12 hours Ongoing Losses =

Hank

Maintenance = 1196 mL/day

Deficit = over 12 hours Ongoing Losses =

1196 mL + 720 mL = 1916 mL/24 hours = 80 mL/hr

2200 mL ÷ 12 hrs = 183 mL/hr

80 mL + 183 mL = 263 mL/hr for first 12 hours, then 80 mL/hour for next 12 hours

Egg Roll, 4 YO CM American Shorthair 2 days post-urethral obstruction, urinary catheter in place -urine output is measured every 4 hours -recent urine output measurement was 32 mL more than he received in IV fluids over those 4 hours

Maintenance = 234 mL/day

Deficit Ongoing Losses

32 mL/4 hours

http://www.vetstreet.com/cats/american-shorthair

Egg Roll -urine output is measured every 4 hours -most recent urine output measurement was 32 mL more than he received in IV fluids

Maintenance = 234 mL/day

Deficit Ongoing Losses

32 mL over 4 hours

http://www.vetstreet.com/cats/american-shorthair

Egg Roll

Maintenance = 234 mL/day

Deficit Ongoing Losses

32 mL over 4 hours

http://www.vetstreet.com/cats/american-shorthair

234 mL ÷ 24 hours = 9.8 mL/hr

32 mL ÷ 4 hours = 8 mL/hr

9.8 mL + 8 mL = 17.8 mL/hr for 4 hrs

Egg Roll http://www.vetstreet.com/cats/american-shorthair

You do not have an IV fluid pump available, but have a 10 drops/mL drip set to use.

What will your drip rate be for Egg Roll?

17.8 mL/hr ≈ 18 mL/hr

Egg Roll http://www.vetstreet.com/cats/american-shorthair

You do not have an IV fluid pump available, but have a 10 drops/mL drip set to use.

What will your drip rate be for Egg Roll? 17.8 mL/hr ≈ 18 mL/hr

Egg Roll http://www.vetstreet.com/cats/american-shorthair

You do not have an IV fluid pump available, but have a 10 drops/mL drip set to use.

What will your drip rate be for Egg Roll? 17.8 mL/hr ≈ 18 mL/hr

Egg Roll http://www.vetstreet.com/cats/american-shorthair

You do not have an IV fluid pump available, but have a 10 drops/mL drip set to use.

What will your drip rate be for Egg Roll?

17.8 mL/hr ≈ 18 mL/hr

Dextrose Supplementation! Commonly administered at

concentrations of 2.5-7.5% ! Concentrations >5% should be delivered

via a central line ! High osmolarity can cause phlebitis

https://www.bemedsupply.com/Dextrose-Water-5-Intravenous-IV-Solution-100ml-p/1-178433.htm https://www.pbsanimalhealth.com/products/dextrose-50-percent-iv-solution

Dextrose Supplementation

Calculation

! concentration you want ! volume you want

! concentration you have ! volume to add

Need to Know: 1. Concentration of dextrose solution 2. Concentration desired 3. Total volume desired

C1×V1 = C2 × V2

Dextrose Supplementation

CalculationNeed to Know: 1. Concentration of dextrose solution 2. Concentration desired 3. Total volume desired

C2 C2

Dextrose Supplementation

Calculation! concentration you want

! volume you want

! concentration you have ! volume to add

Conc. want Conc. have × vol. want = vol. to add

“The concentration you want over the concentration you have, times the volume you want, equals the volume to add.”

You want to add dextrose to your patient’s fluid bag to create a 5% solution. The bag contains 450 mL and

your dextrose solution is 50%. How much do you add?

“The concentration you want over the concentration you have, times the volume you want, equals the volume to add.”

Need to Know: 1. Concentration of dextrose

solution 2. Concentration desired 3. Total volume desired

50%

5% 450 mL

You want to add dextrose to your patient’s fluid bag to create a 5% solution. The bag contains 450 mL and

your dextrose solution is 50%. How much do you add?

“The concentration you want over the concentration you have, times the volume you want, equals the volume to add.”

( 550)× 450 mL= 45 mL

Constant-Rate Infusion

Also known as a CRI

• mg/kg/day • mg/kg/hr • mcg/kg/hr • mcg/kg/min

https://www.unitedadlabel.com/iv-medication-added-label-2-1-2-x-2-1-2 https://m.smiths-medical.com/products/infusion/syringe-infusion/syringe-infusion-pumps/medfusion-3500-syringe-pump https://careforde.com/monet-medical-smiths-medical-medfusion-2001-syringe-pump-reconditioned-2001r3-syringe-pump-3-year-warranty-ea/

http://www.realclear.com/animals/2015/01/21/cranky_critters_who_havent_had_their_morning_coffee_10563.html https://thecatsite.com/ams/why-does-my-cats-mouth-hang-open.33866/

A Concept to Remember

The volume you are administering will depend on two things: 1. Concentration 2. Rate

CRI Calculations

! Used for medications like metoclopramide inj.

Formula: Weight (kg)   __ mg                             kg/day 

OR

• mg/kg/day

• mg/kg/hr • mcg/kg/hr • mcg/kg/min

= __ mg/day

CRI Calculations

! Used for medications like metoclopramide inj.

Formula: Weight (kg)   __ mg     1 mL                           kg/day   __ mg

OR

• mg/kg/day

• mg/kg/hr • mcg/kg/hr • mcg/kg/min

= __ mL/day

Example 

! Petey, 7 kg Rat terrier, vomiting, needs 2 mg/kg/day metoclopramide inj., concentration is 5 mg/mL

 7 kg     2 mg     1 mL             kg/day   5 mg = 2.8 mL/day

https://www.mooremedical.com/index.cfm?/Metoclopramide-Injection/&PG=CTL&CS=HOM&FN=ProductDetail&PID=12139&spx=1 https://www.dogster.com/dogbreed/rat-terrier 

One Step Further…

! Petey, 7 kg Rat terrier, needs 2 mg/kg/day metoclopramide inj., concentration is 5 mg/mL, to be added to 1 L LRS and delivered at a rate of 22 mL/hr

! How many mL of metoclopramide needs to be added to the bag?

 7 kg     2 mg     1 mL    1 day                kg/day   5 mg    24 hrs     = 0.12 mL/hr

https://www.mooremedical.com/index.cfm?/Metoclopramide-Injection/&PG=CTL&CS=HOM&FN=ProductDetail&PID=12139&spx=1 https://www.dogster.com/dogbreed/rat-terrier 

One Step Further

! Petey, 7 kg Rat terrier, needs 2 mg/kg/day metoclopramide inj., concentration is 5 mg/mL, to be added to 1 L LRS and delivered at a rate of 22 mL/hr

! How many mL of metoclopramide needs to be added to the bag?

     0.12 mL/hr

https://www.mooremedical.com/index.cfm?/Metoclopramide-Injection/&PG=CTL&CS=HOM&FN=ProductDetail&PID=12139&spx=1 https://www.dogster.com/dogbreed/rat-terrier 

One Step Further…

! Petey, 7 kg Rat terrier, needs 2 mg/kg/day metoclopramide inj., concentration is 5 mg/mL, to be added to 1 L LRS and delivered at a rate of 22 mL/hr

! How many mL of metoclopramide needs to be added to the bag?

     

https://www.mooremedical.com/index.cfm?/Metoclopramide-Injection/&PG=CTL&CS=HOM&FN=ProductDetail&PID=12139&spx=1 https://www.dogster.com/dogbreed/rat-terrier 

(1000 mL22mL/hr )=45.45 hrs/bag

One Step Further…

! Petey, 7 kg Rat terrier, needs 2 mg/kg/day metoclopramide inj., concentration is 5 mg/mL, to be added to 1 L LRS and delivered at a rate of 22 mL/hr

! How many mL of metoclopramide needs to be added to the bag?

 7 kg     2 mg     1 mL    1 day    45.5 hrs             kg/day   5 mg    24 hrs      bag = 5.3 mL/bag

https://www.mooremedical.com/index.cfm?/Metoclopramide-Injection/&PG=CTL&CS=HOM&FN=ProductDetail&PID=12139&spx=1 https://www.dogster.com/dogbreed/rat-terrier 

CRI Calculations ! Used for medications like diazepam, midazolam,

furosemide

Formula: Weight (kg)   __ mg     1 mL                                 kg/hr    __ mg   

• mg/kg/day

• mg/kg/hr • mcg/kg/hr • mcg/kg/min

= __ mL/hr

Example 

! June Bug, 16 kg mixed breed canine, uncontrolled status epilepticus, needs 0.5 mg/kg/hr diazepam inj., available concentration is 5 mg/mL

https://www.petcha.com/about-the-mixed-dog-breed/  https://www.acesurgical.com/diazepam-5mg-ml-10ml-mdv-injection.html 

Example 

! June Bug, 16 kg mixed breed canine, uncontrolled status epilepticus, needs 0.5 mg/kg/hr diazepam inj., available concentration is 5 mg/mL

 16 kg  0.5 mg  1 mL               kg/hr    5 mg   = 1.6 mL/hr

https://www.petcha.com/about-the-mixed-dog-breed/  https://www.acesurgical.com/diazepam-5mg-ml-10ml-mdv-injection.html 

CRI Calculations• mg/kg/day • mg/kg/hr

• mcg/kg/hr • mcg/kg/min

! Used for medications like fentanyl

Formula: Weight (kg)  __ mcg                              kg/hr      = __ mcg/hr

https://www.askideas.com/20-very-funny-thumb-pictures-and-images/

CRI Calculations• mg/kg/day • mg/kg/hr

• mcg/kg/hr • mcg/kg/min

! Used for medications like fentanyl

! Formula: Weight (kg)  __ mcg      1 mg                                  kg/hr     1000 mcg   = __ mg/hr

https://www.trendhunter.com/trends/cat-photography

CRI Calculations• mg/kg/day • mg/kg/hr

• mcg/kg/hr • mcg/kg/min

! Used for medications like fentanyl

! Formula: Weight (kg)  __ mcg      1 mg        1 mL                           kg/hr     1000 mcg    __ mg  = __ mL/hr

Example 

! Mater, 48 kg Great Dane, post-operative limb amputation, needs 4 mcg/kg/hr fentanyl inj., concentration is 0.05 mg/mL

 

https://www.buyemp.com/product/fentanyl-citrate-250-mcg-5-ml-injection-usp-cii  https://www.google.com/search?q=great+dane+osteosarcoma&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjj8tDAu4zhAhUFzIMKHbNlAfQQ_AUIDigB&biw=1920&bih=937#imgrc=wcfyA_nT2OgT_M: 

Example 

! Mater, 48 kg Great Dane, post-operative limb amputation, needs 4 mcg/kg/hr fentanyl inj., concentration is 0.05 mg/mL

 48 kg   4 mcg     1 mg                     kg/hr    1000 mcg  = 0.192 mg/hr

https://www.buyemp.com/product/fentanyl-citrate-250-mcg-5-ml-injection-usp-cii  https://www.google.com/search?q=great+dane+osteosarcoma&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjj8tDAu4zhAhUFzIMKHbNlAfQQ_AUIDigB&biw=1920&bih=937#imgrc=wcfyA_nT2OgT_M: 

Example 

! Mater, 48 kg Great Dane, post-operative limb amputation, needs 4 mcg/kg/hr fentanyl inj., concentration is 0.05 mg/mL

 48 kg   4 mcg       1 mg        1 mL               kg/hr    1000 mcg  0.05 mg = 3.8 mL/hr

https://www.buyemp.com/product/fentanyl-citrate-250-mcg-5-ml-injection-usp-cii  https://www.google.com/search?q=great+dane+osteosarcoma&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjj8tDAu4zhAhUFzIMKHbNlAfQQ_AUIDigB&biw=1920&bih=937#imgrc=wcfyA_nT2OgT_M: 

CRI Calculations• mg/kg/day • mg/kg/hr • mcg/kg/hr

• mcg/kg/min

! Used for medications like ketamine, lidocaine, norepinephrine, epinephrine, vasopressin

Formula: Weight (kg)  __ mcg        1 mg        1 mL                           kg/min   1000 mcg    __ mg  = __ mL/min

CRI Calculations• mg/kg/day • mg/kg/hr • mcg/kg/hr

• mcg/kg/min

! Used for medications like ketamine, lidocaine, norepinephrine, epinephrine, vasopressin

Formula: Weight (kg)  __ mcg        1 mg        1 mL                           kg/min   1000 mcg    __ mg  = __ mL/min

Example 

! Maizy, 23 kg Labrador retriever, HBC with ventricular tachycardia, needs 40 mcg/kg/min lidocaine inj., concentration is 20 mg/mL

 23 kg   40 mcg      1 mg                   kg/min   1000 mcg  = 0.92 mg/min

https://www.thelabradorsite.com/dog-cone/  https://entirelypetspharmacy.com/lidocaine-injectable-100ml.html 

Example 

! Maizy, 23 kg Labrador retriever, HBC with ventricular tachycardia, needs 40 mcg/kg/min lidocaine inj., concentration is 20 mg/mL

 23 kg   40 mcg      1 mg        1 mL              kg/min   1000 mcg  20 mg = 0.05 mL/min

https://www.thelabradorsite.com/dog-cone/  https://entirelypetspharmacy.com/lidocaine-injectable-100ml.html 

Questions?